Pulse Electrothermal Deicing Of Complex Shapes

ABSTRACT

A pulse electrothermal deicing apparatus comprises at least one complex shape characterized by a thickness profile configured to generate uniform power per unit area to melt an interfacial layer of ice. A method of optimizing thicknesses of complex shapes for a pulse electrothermal deicing system includes assigning initial estimates of the pulse electrothermal deicing system parameters. A temperature distribution, a temperature range and a refreezing time produced by a deicing pulse are modeled. Shape thicknesses are adjusted according to the temperature range, deicing pulse parameters are adjusted according to the deicing pulse, and the modeling and adjusting is repeated until the temperature range and the refreezing time are within predetermined limits.

RELATED APPLICATIONS

This application claims the benefit of priority to commonly-owned and copending U.S. Provisional Patent Application No. 60/802,407, filed 22 May 2006. This application is also a continuation-in-part of commonly-owned and copending PCT/US2006/002283, filed 24 Jan. 2006, which claims the benefit of priority to U.S. Provisional Patent Applications Nos. 60/646,394, filed 24 Jan. 2005, 60/646,932, filed 25 Jan. 2005, and 60/739,506, filed 23 Nov. 2005. This application is also a continuation-in-part of commonly-owned and copending U.S. patent application Ser. No. 11/571,231, filed 22 Dec. 2006, which claims the benefit of priority to PCT/US2005/022035, filed 22 Jun. 2005, which claims the benefit of priority to U.S. Provisional Patent Applications Nos. 60/581,912, filed 22 Jun. 2004, 60/646,394, filed 24 Jan. 2005, and 60/646,932, filed 25 Jan. 2005. This application is also a continuation-in-part of commonly-owned and copending U.S. patent application Ser. No. 11/338,239, filed 24 Jan. 2006, which claims the benefit of priority to U.S. patent application Ser. No. 10/939,289, now U.S. Pat. No. 7,034,257, filed 10 Sep. 2004, which is a divisional application that claims the benefit of priority to U.S. patent application Ser. No. 10/364,438, now U.S. Pat. No. 6,870,139, filed 11 Feb. 2003, which claims the benefit of priority to U.S. Provisional Patent Applications Nos. 60/356,476, filed 11 Feb. 2002, 60/398,004, filed 23 Jul. 2002, and 60/404,872, filed 21 Aug. 2002. All of the above-identified patent applications are incorporated herein by reference.

BACKGROUND

Deicing by melting or detaching ice with electrically generated heat (Joule heat) has many applications. Some of these applications benefit from minimizing the energy that is applied to the ice and/or object to which the ice is adhered. For example, generation of more heat than is necessary to melt or at least detach ice requires excess expenditure of energy. In some applications, such as in ice making or deicing of refrigeration equipment, the expenditure of extra energy in detaching ice is especially disadvantageous; not only is the ice melting energy expended, but still more energy may be expended by a cooling system to re-cool the part of the system that the ice was detached from.

SUMMARY

In one embodiment, a pulse electrothermal deicing apparatus comprises at least one complex shape characterized by a thickness profile configured to generate uniform power per unit area to melt an interfacial layer of ice.

In one embodiment, a method of optimizing thicknesses of complex shapes for a pulse electrothermal deicing system includes: assigning size and geometry to each shape of the pulse electrothermal deicing system and connectivity of the shapes; assigning initial thicknesses to each shape; assigning an initial estimate to a deicing pulse duration; modeling a temperature distribution over the surface of each shape based upon the deicing pulse duration and the thickness of each shape; determining a refreezing time for each shape after application of the deicing pulse; adjusting the thickness of each shape based upon the modeled temperature distribution if the modeled temperature distribution is not within a desired tolerance; adjusting the deicing pulse duration based upon the determined refreezing time and if the determined refreezing time is not within defined limits; and repeating the steps of modeling, determining and adjusting until the temperature distribution is within the desired tolerance and the refreezing time is within defined limits.

In one embodiment, a pulse electrothermal deicing apparatus comprises at least one axially symmetric complex shape characterized by a thickness profile configured to generate uniform power per unit area to melt an interfacial layer of ice.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows one exemplary pulse electrothermal deicing (PETD) apparatus including a flat plate, in accordance with an embodiment.

FIG. 2 shows one exemplary PETD apparatus including a cylinder, in accordance with an embodiment.

FIG. 3 shows one exemplary PETD apparatus including a cone, in accordance with an embodiment.

FIG. 4 shows one exemplary PETD apparatus including a sphere, in accordance with an embodiment.

FIG. 5 shows one exemplary PETD apparatus including a crescent, in accordance with an embodiment.

FIG. 6 shows a rendition of an exemplary ice tray for a residential icemaker having an axially symmetric shape.

FIG. 7 is a flowchart illustrating one exemplary method for optimizing thicknesses of complex, conductive shapes in a design of a PETD system, in accordance with an embodiment.

DETAILED DESCRIPTION OF THE DRAWINGS

Pulse electrothermal deicing (PETD) may be utilized to separate “ice” from an object by melting at least an interfacial layer of the ice. As used herein, the term “ice” refers to any of ice, snow, frost and other forms of frozen water, with or without admixed substances. An “interfacial layer of ice” shall refer to a thin layer of ice proximate to the object. Melting of the interfacial layer of ice is generally sufficient to detach bulk ice (i.e., the unmelted portion of the ice) from the object. An interfacial layer of ice may have a thickness of less than about 5 centimeters, preferably less than about 3 centimeters, more preferably between about one centimeter and one micron, and most preferably between about one millimeter and one micron. It will be appreciated that energy applied to heat the interfacial ice will also heat a portion of the object in contact with the interfacial ice. It is desirable that heat diffuses a distance of less than about 5 centimeters into the object and/or ice, preferably less than about 3 centimeters into the object and/or ice, more preferably between about one centimeter and one micron into the object and/or ice, and most preferably between about one millimeter and one micron into the object and/or ice.

Energy expended during PETD is advantageously minimized by providing a uniformly melted interfacial layer. Excessively thick melted interfacial layers correspond to higher deicing temperatures, and represent wasted energy in the deicing process; that is, more energy is applied than is needed to separate bulk ice from the object. For example, in an icemaker, a “hot spot” created during deicing requires re-cooling, after deicing, before ice making can resume at that spot; this lowers yield of the ice making process by melting more of the intended product than necessary. Excessively thin melted interfacial layers correspond to a risk that the bulk ice will refreeze to the object before the ice can be removed.

In order to optimize energy expenditure for deicing, an apparatus utilizing PETD should provide an approximately constant density of heating power per surface area of the interfacial ice layer. However, a constant density of heating power per surface area can be difficult to achieve when an object to be deiced has a complex shape. As used herein, a “complex shape” is a portion of an object having one or more non-uniformly thick walls. The complex shape can be described by a “thickness profile”, which defines the thickness of the wall over a distance (e.g., from one point on the object to another point on the object).

A heating layer of an object is characterized by an electrical resistivity ρ and a thickness t. When heating power per unit area W (in W/m²) is applied, the following relationship applies:

$\begin{matrix} {W = {{E \cdot I_{S}} = {\frac{E^{2} \cdot t}{\rho} = \frac{\rho \cdot I_{S}^{2}}{t}}}} & {{Eq}.\mspace{14mu} (1)} \end{matrix}$

where E is an electric field strength (V/m) developed through the heating layer by the application of an electric current density I_(S) (A/m). In order to keep W constant at various portions of the heating layer, the following relationship further applies:

$\begin{matrix} {t = {{\frac{W \cdot \rho}{E^{2}}\mspace{14mu} {or}\mspace{14mu} t} = \frac{\rho \cdot I_{S}^{2}}{W}}} & {{Eq}.\mspace{14mu} (2)} \end{matrix}$

Equation (2) is approximate because it does not take into account dependence of heat capacitance of the heating layer on the object thickness. However, Eq. (2) is very useful because heat capacitance is usually a very small term in total PETD energy requirements as compared to heat capacitance of ice, underlying structure, and latent heat of the melted interfacial ice layer.

FIG. 1 shows one exemplary PETD apparatus 10(1) including a flat plate 40(1). FIG. 1 may not be drawn to scale. A power supply 20(1) connects to flat plate 40(1) through a switch 30(1) to supply power to plate 40(1) for deicing. Length L and thickness t of plate 40(1) are indicated in FIG. 1. Where power supply 20(1) supplies a voltage V, the power W supplied by power supply 20(1) may be expressed in terms of power per unit area as:

$\begin{matrix} {W = \frac{V^{2} \cdot t}{\rho \cdot L^{2}}} & {{Eq}.\mspace{14mu} (3)} \end{matrix}$

FIG. 2 shows one exemplary PETD apparatus 10(2) including a cylinder 40(2). FIG. 2 may not be drawn to scale. A power supply 20(2) connects to cylinder 40(2) through a switch 30(2) to supply power to cylinder 40(2) for deicing. Length L and thickness t of cylinder 40(2) are indicated in FIG. 2. Where power supply 20(2) supplies a voltage V, the power W supplied by power supply 20(2) may be expressed in terms of power per unit area as shown in Eq. (3), which describes objects having constant thickness.

FIG. 3 shows a cross-section of one exemplary PETD apparatus 10(3) including a cone 40(3). FIG. 3 may not be drawn to scale. A power supply 20(3) connects through a switch 30(3) to supply power to cone 40(3) for deicing. A linear dimension x, an angle θ with respect to the x axis, and a thickness t of cone 40(3) are indicated in FIG. 3. Note that thickness t varies with position along the x axis of cone 40(3). Where power supply 20(3) supplies a voltage V and a current I₀, thickness t, required to provide a constant power W per unit area, may be expressed as:

$\begin{matrix} {t = \frac{\rho \cdot I_{0}^{2}}{{4{\pi^{2} \cdot x^{2}}}{\cdot {\tan^{2}(\theta)} \cdot W}}} & {{Eq}.\mspace{14mu} (4)} \end{matrix}$

FIG. 4 shows a cross-section of one exemplary PETD apparatus 10(4) including a sphere 40(4). FIG. 4 may not be drawn to scale. A power supply 20(4) connects to sphere 40(4) through a switch 30(4) to supply power to sphere 40(4) for deicing. A radius R, an angle θ with respect to an axis along which power is supplied, and a thickness t of sphere 40(4) are indicated in FIG. 4. Note that thickness t of sphere 40(4) varies with angle θ. Where power supply 20(4) supplies a voltage V and a current I₀, thickness t, required to provide a constant power W per unit area, may be expressed as:

$\begin{matrix} {t = \frac{\rho \cdot I_{0}^{2}}{4{\pi^{2} \cdot R^{2} \cdot {\sin^{2}(\theta)} \cdot W}}} & {{Eq}.\mspace{14mu} (5)} \end{matrix}$

FIG. 5 shows one exemplary PETD apparatus 10(5) including a crescent 40(5). FIG. 5 may not be drawn to scale. Crescent 40(5) may be generated by revolving a line about an axis of rotation. Such shapes may be useful, for example, in icemakers wherein a shape is (1) filled with liquid water, (2) cooled until the water freezes to form ice, (3) rotated so that the ice faces downward, and (4) heated with a deicing pulse to release the ice from the shape. A power supply 20(5) connects through a switch 30(5) to supply power to crescent 40(5) for deicing. A linear dimension x, an offset value R(x) that is a function of position on the x axis, and a thickness t of crescent 40(5) are indicated in FIG. 5. Note that thickness t of shape 40(5) varies with R(x). It can be shown that if power supply 20(5) supplies a voltage V and current I₀, thickness t, required to provide a constant power W per unit area, may be expressed as:

$\begin{matrix} {t = \frac{\rho \cdot I_{0}^{2}}{4{\pi^{2} \cdot {R^{2}(x)} \cdot W}}} & {{Eq}.\mspace{14mu} (6)} \end{matrix}$

Several technologies may be utilized to manufacture any of the shapes 40 described above, including but not limited to die casting, injection molding, consecutive applications of conductive paint or other coatings and machining.

FIG. 6 shows a rendition of an ice tray 50 for a residential icemaker. An icemaker utilizing ice tray 50 may be made of a thermally and electrically conductive composite material, such as E5101 by CoolPolymers, Inc. An inner shape 40(6) of ice tray 50 is axially symmetric. To form ice, tray 50 is disposed with inner shape 40(6) facing upward. Tray 50 is then filled with water. After the water freezes into ice, tray 50 is rotated about its long axis by about 120° and a two second pulse of electrical power is applied across copper bus bars disposed on terminal ends 60(1), 60(2) of tray 50. The electrical power heats tray 50 uniformly to a temperature just above the melting point of the ice, thus melting an interfacial layer of the ice. The ice then slides off tray 50 and into a collection bin (not shown). It is appreciated that tray 50 includes a complex, variable thickness. The thickness may be calculated utilizing Eq. (6), then the thickness may be adjusted at certain locations, such as corners, according to a method described below.

FIG. 7 is a flowchart illustrating one exemplary method 100 for optimizing thicknesses of complex, conductive shapes in a PETD system design. It will be appreciated that some or all of the steps illustrated in FIG. 7 may be performed by a computer under control of software instructions; alternatively, some or all of the steps of FIG. 7 may be performed by a human. In step 102, method 100 assigns a size and geometry type to each shape of the deicing system, and connections among the shapes. In step 104, method 100 assigns an initial thickness configuration to each shape; such configuration may include a fixed thickness (e.g., as shown in FIGS. 1 and 2, and Eq. (3)) and/or a thickness that varies as a function of position and/or angle (e.g., as shown in FIGS. 3-5 and Eqs. (4)-(6)) where the shape is complex. In step 106, deicing pulse parameters, such as voltage or current supplied, and an initial estimate of a deicing pulse duration are assigned. In step 108, a temperature distribution, a temperature range and a refreezing time achieved for the specified shapes with the specified deicing pulse are determined. Step 108 may be performed, for example, utilizing finite element method modeling using a package such as FEMLAB 3.1 by Comsol, Inc. Step 110 is a decision that determines whether or not the temperature range is within a specified tolerance. If the temperature range is outside of the specified tolerance (i.e., there is a larger than desired difference between the lowest temperature and the highest temperature generated by the deicing pulse), then shapes are thickened or thinned in steps 112 and 114 according to whether the modeled temperature of the shape is too high or too low, respectively. Step 116 is a decision. In step 116, the refreezing time is compared to specified minimum and maximum limits. If the refreezing time is too short (i.e., below the specified minimum limit), the deicing pulse is lengthened in step 118; if the refreezing time is too long (i.e., above the specified maximum), the deicing pulse is shortened in step 120. It will be appreciated that power parameters of the deicing pulse may also be modified, such as to provide more or less power, instead of or in addition to changing the duration of the deicing pulse. If any of the shape thicknesses and the refreezing times changed in steps 112, 114, 118 and/or 120, the method returns to step 108; otherwise, the method finishes and outputs a set of optimized thickness and deicing pulse parameters in step 122.

The changes described above, and others, may be made in the pulse electrothermal deicers for complex shapes and associated methods described herein without departing from the scope hereof. For example, variations in heating may be provided by varying electrical resistivity, as opposed to thicknesses of, complex shapes. The principles described herein are also applicable to configurations such as evaporator plates of refrigeration or air conditioning systems that may require periodic deicing. It should thus be noted that the matter contained in the above description or shown in the accompanying drawings should be interpreted as illustrative and not in a limiting sense. The following claims are intended to cover all generic and specific features described herein, as well as all statements of the scope of the present methods and systems, which, as a matter of language, might be said to fall there between. 

1. Pulse electrothermal deicing apparatus comprising at least one complex shape characterized by a thickness profile configured to generate uniform power per unit area to melt an interfacial layer of ice.
 2. Pulse electrothermal deicing apparatus of claim 1, further comprising a power supply and a switch to alternatively connect and disconnect the power supply from the complex shape.
 3. Pulse electrothermal deicing apparatus of claim 1, wherein the complex shape comprises a cone, and thickness t of the cone varies according to the $t = \frac{\rho \cdot I_{0}^{2}}{4{\pi^{2} \cdot x^{2} \cdot {\tan^{2}(\theta)} \cdot W}}$ wherein the cone is characterized by a linear dimension x along an x-axis and an angle θ with respect to the x axis, and the power supply supplies a current I₀ to provide a power W per unit area.
 4. Pulse electrothermal deicing apparatus of claim 1, wherein the complex shape comprises a sphere, and thickness t of the sphere varies according to the equation: $t = \frac{\rho \cdot I_{0}^{2}}{4{\pi^{2} \cdot R^{2} \cdot {\sin^{2}(\theta)} \cdot W}}$ wherein the sphere is characterized by a radius R and an angle θ with respect to an axis along which power is supplied, and the power supply supplies a current I₀ to provide a power W per unit area.
 5. Pulse electrothermal deicing apparatus of claim 1, wherein the complex shape comprises a crescent, and thickness t of the sphere varies according to the equation: $t = \frac{\rho \cdot I_{0}^{2}}{4{\pi^{2} \cdot {R^{2}(x)} \cdot W}}$ wherein the crescent is characterized by a linear dimension x and an offset value R(x), and the power supply supplies a current I₀ to provide a power W per unit area.
 6. Pulse electrothermal deicing apparatus of claim 1, the complex shape formed by one of die casting, injection molding, machining, and successive application of conductive layers.
 7. A method of optimizing thicknesses of complex shapes for a pulse electrothermal deicing system, comprising: assigning size and geometry to each shape of the pulse electrothermal deicing system and connectivity of the shapes; assigning initial thicknesses to each shape; assigning an initial estimate to a deicing pulse duration; modeling a temperature distribution over the surface of each shape based upon the deicing pulse duration and the thickness of each shape; determining a refreezing time for each shape after application of the deicing pulse; adjusting the thickness of each shape based upon the modeled temperature distribution if the modeled temperature distribution is not within a desired tolerance; adjusting the deicing pulse duration based upon the determined refreezing time and if the determined refreezing time is not within defined limits; and repeating the steps of modeling, determining and adjusting until the temperature distribution is within the desired tolerance and the refreezing time is within defined limits.
 8. The method of claim 7, the step of adjusting the thickness comprising: increasing the thickness of the shape where the temperature distribution is higher than the desired tolerance; and decreasing the thickness of the shape where the temperature distribution is lower than the desired tolerance.
 9. The method of claim 7, the step of assigning initial thicknesses to each shape comprising assigning a fixed thickness to each shape.
 10. The method of claim 7, the step of assigning initial thicknesses to each shape comprising assigning a variable thickness to each shape.
 11. The method of claim 7, the step of adjusting the deicing pulse duration comprising shortening the duration if the determined refreezing time is above the defined limits.
 12. The method of claim 7, the step of adjusting the deicing pulse duration comprising lengthening the duration if the determined refreezing time is below the defined limits.
 13. Pulse electrothermal deicing apparatus comprising at least one axially symmetric complex shape characterized by a thickness profile configured to generate uniform power per unit area to melt an interfacial layer of ice.
 14. Pulse electrothermal deicing apparatus of claim 13, further comprising a power supply and a switch to alternatively connect and disconnect the power supply from the axially symmetric complex shape.
 15. Pulse electrothermal deicing apparatus of claim 13, wherein the axially symmetric complex shape comprises a cone, and thickness t of the cone varies according to the equation: $t = \frac{\rho \cdot I_{0}^{2}}{4{\pi^{2} \cdot x^{2} \cdot {\tan^{2}(\theta)} \cdot W}}$ wherein the cone is characterized by a linear dimension x along an x-axis and an angle θ with respect to the x axis, and the power supply supplies a current I₀ to provide a power W per unit area.
 16. Pulse electrothermal deicing apparatus of claim 13, wherein the axially complex shape comprises a sphere, and thickness t of the sphere varies according to the equation: $t = \frac{\rho \cdot I_{0}^{2}}{4{\pi^{2} \cdot R^{2} \cdot {\sin^{2}(\theta)} \cdot W}}$ wherein the sphere is characterized by a radius R and an angle θ with respect to an axis along which power is supplied, and the power supply supplies a current I₀ to provide a power W per unit area.
 17. Pulse electrothermal deicing apparatus of claim 13, wherein the axially symmetric complex shape comprises a crescent, and thickness t of the sphere varies according to the equation: $t = \frac{\rho \cdot I_{0}^{2}}{4{\pi^{2} \cdot {R^{2}(x)} \cdot W}}$ wherein the crescent is characterized by a linear dimension x and an offset value R(x), and the power supply supplies a current I₀ to provide a power W per unit area.
 18. Pulse electrothermal deicing apparatus of claim 13, the axially symmetric complex shape formed by one of die casting, injection molding, machining, and successive application of conductive layers. 